GME asked 1 year ago
From a photograph of a homeowner using a snowblower, it is determined that the radius of curvature of the trajectory of the snow was 30 ft as the snow left the discharge chute at A. Determine (a) the discharge velocity vA of the snow, (b) the radius of curvature of the trajectory at its maximum height.
Fig. P11.143
Sazid Ahmad answered 1 year ago
Step: 1
a)
Show the acceleration of snow, tangential, and normal component of acceleration using vector diagram as in Figure (1).
Step: 2
In Figure (1), snow is acted upon by acceleration due to gravity. Direction of tangential component of acceleration is against the direction of motion since speed of snow decreases. Direction of normal component of acceleration is acting towards the centre of curvature.
Write the normal component of acceleration vector a as:
…… (1)
Here, magnitude of normal component of acceleration vector is 
and magnitude of acceleration is a.
Choose magnitude of acceleration vector as 
.
Substitute 
for a in Equation (1) to find 
.
Thus, magnitude of normal component of acceleration vector is 
.
Step: 3
Write the normal component of acceleration of an object in circular motion as the ratio between the square of the speed and radius of curvature of the path.
…… (2)
Here, normal component of acceleration of object is 
, speed of the snow is v, and radius of curvature is 
.
Rewrite Equation (2) as:
…… (3)
Substitute 
for 
and 30ft for 
in Equation (3) to find v.
Hence, magnitude of discharge velocity is 
at an angle of 
.
Step: 4
b)
Write x-component of 
as:
…… (4)
Here, x-component of 
is 
.
Substitute 
for 
in Equation (4).
Thus, x-component of 
is 
. Maximum height of the trajectory depends on the x-component of 
and the only acceleration that acts on the snow is acceleration due to gravity. Thus, 
.
Step: 5
Rewrite Equation (2) to find the radius of curvature of trajectory at its maximum height.
…… (5)
Substitute 
for 
and 
for a in Equation (5).
Hence, the radius of curvature of trajectory at its maximum height is 
.